A Modified “Best Maximum Likelihood” Estimator of Line Regression with Errors in Both Variables: An Application for Estimating Genetic Admixture

The problem of estimation when both variables are subject to error in a linear regression model has been discussed in the literature and it has wide applications in econometrics and other social sciences. In this paper we consider the relaxation of the assumption of homoscedasticity and introduce the covariance structure of errors of measurements in the analysis to obtain a Modified Best Maximum Likelihood (MBML) estimator of the regression coefficient. We also provide an application of the above modification to estimate the extent of genetic contribution of a parental population in an admixed population. With data on frequencies of “unique” African and Caucasian alleles in US Blacks, it is shown that US Blacks have 30.9·2.2 percent genes that are of Caucasian origin.